Tachyon inflation with steep potentials

Within the framework of tachyon inflation, we consider different steep potentials and check their viability in light of the Planck 2015 data. We see that in this scenario, the inverse power-law potential $V(\phi)=V_{0}(\phi/\phi_{0})^{-n}$ with $n=2$ leads to the power-law inflation with the scale factor $a(t)\propto t^{q}$ where $q>1$, while with $n<2$, it gives rise to the intermediate inflation with the scale factor $a(t)\propto\exp\left(At^{f}\right)$ where $A>0$ and $0<f<1$. We find that, although the inverse power-law potential with $n\leq 2$ is completely ruled out by the Planck 2015 data, the result of this potential for $n>2$ can be compatible with the 95\% CL region of Planck 2015 TT, TE, EE+lowP data. We further conclude that the exponential potential $V(\phi)=V_{0}e^{-\phi/\phi_{0}}$, the inverse $\cosh$ potential $V(\phi)=V_{0}/\cosh(\phi/\phi_{0})$, and the mutated exponential potential $V(\phi)=V_{0}\left[1+(n-1)^{-(n-1)}(\phi/\phi_{0})^{n}\right]e^{-\phi/\phi_{0}}$ with $n=4$, can be consistent with the 95\% CL region of Planck 2015 TT, TE, EE+lowP data. Moreover, using the $r-n_s$ constraints on the model parameters, we also estimate the running of the scalar spectral index $dn_{s}/d\ln k$ and the local non-Gaussianity parameter $f_{{\rm NL}}^{{\rm local}}$. We find that the lower and upper bounds evaluated for these observables are compatible with the Planck 2015 results.